nLab
magic pyramid

Contents

Context

Gravity

Super-Geometry

Contents

Idea

The classification of pure supergravity theories in dimensions 3,4,6,10 and 4,5,7,11 is parameterized by the real normed division algebras, while the classification of super Yang-Mills theories is parameterized by pairs of real normed division algebras, see at supersymmetry and division algebra and at spin representation.

Combining this yields a classification of the extended super Einstein-Yang-Mills theories by triples of real normed division algebras. called a magic pyramid of supergravity theories (ABDHN 13).

(from ABDHN 13, p. 3)

In this diagram vertical axis labels the spacetime division algebra (hence vertical label \mathbb{R} corresponds to d=2+1d = 2+1, vertical label \mathbb{C} to d=3+1d = 3+1, \mathbb{H} to d=5+1d = 5+1 and 𝕆\mathbb{O} to d=9+1d = 9+1) , while the horizontal axes label the algebras associated with the number of left and right supersymmetries. The entries display the corresponding U-duality groups. Each horizontal level is a “magic square”.

References

based on

Last revised on November 20, 2017 at 14:13:56. See the history of this page for a list of all contributions to it.